Our reduction directly extends the results for linear bandits with adversarial corruption to the contextual setting while maintaining the same regret bounds up to \(\log \)  factors. This leads to \(\tilde{O}(d\sqrt{T}+d^{1.5}C)\)  high probability regret bound as opposed to the best known \(\tilde{O}(d^{4.5}\sqrt{T}+d^4C)\)  regret bound. It was shown in [1]} that PE with modified confidence intervals achieves an \(\tilde{O}(d\sqrt{T}+d^{1.5}C)\)  high probability regret bound for unknown corruption \(C\) . A model selection based approach in [2]} that uses PE as a subroutine is shown to generalize this result for unknown \(C\)  without changing the regret bound except for \(\log \)  factors. By adapting the confidence intervals of PE to account for the known \(\epsilon _m\)  misspecification the \(\tilde{O}(d\sqrt{T}+d^{1.5}C)\)  high probability regret bound extends for a model with \(O(\sqrt{d\log T/T})\)  misspecification and known corruption \(C\) . We will modify the PE confidence interval to be
\(\gamma _m=8d\sqrt{\log (T) / t^{(m)}}+\frac{2C(4d\log \log d + 18)}{T_m}\sqrt{8d}.\) 
